Question

To solve first order linear differential equation, we use following steps
(i) Write the solution of the given differential equation as
$y(IF)=∫(Q×IF)dx+C$
(ii) Write the given differential equation in the form $\frac{dy}{dx}+Py=Q$, where $P$ and $Q$ are constants or functions of $x$ only.
(iii) Find the integrating factor $(IF)=e^{∫Pdx}$.
The correct order of the above steps is

• A. (ii), (iii), (i)
• B. (ii), (i), (iii)
• C. (iii), (i), (ii)
• D. (i), (iii), (ii)

Answer 1

Answer: (A)

Steps involved to solve first order linear differential equation.
(i) Write the given differential equation in the form $\frac{dy}{dx}+Py=Q$
where $P,Q$ are constants or functions of $x$ only.
(ii) Find the Integrating Factor (IF) $=e^{∫Pdx}$.
(iii) Write the solution of the given differential equation as
$y(F)=∫(Q×IF)dx+C$
Note In case, the first order linear differential equation is in the form $\frac{dx}{dy}+P_{1}x=Q_1$, where $P_1$ and $Q_1$ are constants or functions of $y$ only. Then, IF $=e^{∫\text{ Rdy }}$ and the solution of the differential equation is given by
$xâ‹\dots (IF)=∫\left(Q_1×IF\right)dy+C$